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NOMBRES somme de Premiers consécutifs On
donne les nombres premiers consécutifs
et, en final, leur somme. Pour tous les nombres n:
|
Anglais: sum of a run of consecutive prime numbers
Les nombres m
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Somme des nombres premiers Cas de
divisibilités singulières. P = 71 divise la somme des premiers jusqu'à 71. En effet: 639 = 71 x 9 Même
propriété pour P = 2 et P = 5. Le
suivant après 71 est:
369 119. Somme de tous les nombres
Tous les nombres
impairs divisent la somme des nombres inférieurs à eux (ou avec eux compris). Somme des nombres composés
Les seuls
cas (1, 22 et 25) jusqu'au prochain composé: 2 745. |
Table des nombres premiers, leur rang (r), le cumul de la somme et ce cumul divisé par P. Exemple de lecture: le 4e nombre premier (5) divise la somme des nombres
premiers jusqu'a 5 (10).
Cas des sommes de premiers divisibles par le
dernier terme de la somme 1, 2, 2, 1 3, 5, 10, 2
20, 71, 639, 9 31464, 369119, 5537154119, 15001 En jaune rappel des cas vus ci-dessus. Aucun autre cas jusqu'à 1 million de premiers. |
|
|
Moyenne de la somme des premiers consécutifs On note
les cas où cette moyenne est un nombre entier. Par
exemple, la somme des 23 premiers nombres premiers 2 + 3 + 5 + … + 83 = 874 et
la moyenne est 874 / 23 = 38, qui est un nombre entier. |
Les cinq premières valeurs
La suite 1, 23, 53, 853, 11869, 117267, 339615, 3600489, 96643287, 2664167025,
43435512311, 501169672991, 745288471601 … |
Voir Nombres
composés / Sommes des
premiers en 100k, 1000k ou 10000k
|
|
||
|
Exemple de lecture 1980 = 137 + 138 + … + 193, une succession
de Q = 12 nombres premiers commençant par PP = 137 et finissant
par PD = 193. Les nombres en rouge sont premiers. Les nombres marqués avec un
slash (/) ou absents sont composés
sans être atteints par une somme de premiers consécutifs. |
De 1980 à
2030
|
|
Voir Nombre 2016
|
Deux |
Trois |
Qu |
Cinq |
|
0, 2, 2 2, 3, 5 3, 5, 8 5, 7, 12 7, 11, 18 11, 13, 24 13, 17, 30 17, 19, 36 19, 23, 42 23, 29, 52 29, 31, 60 31, 37, 68 37, 41, 78 41, 43, 84 43, 47, 90 47, 53, 100 53, 59, 112 59, 61, 120 61, 67, 128 67, 71, 138 71, 73, 144 73, 79, 152 79, 83, 162 83, 89, 172 89, 97, 186 97, 101, 198 101, 103, 204 103, 107, 210 107, 109, 216 109, 113, 222 113, 127, 240 127, 131, 258 131, 137, 268 137, 139, 276 139, 149, 288 149, 151, 300 151, 157, 308 157, 163, 320 163, 167, 330 167, 173, 340 173, 179, 352 179, 181, 360 181, 191, 372 191, 193, 384 193, 197, 390 197, 199, 396 199, 211, 410 211, 223, 434 223, 227, 450 227, 229, 456 229, 233, 462 233, 239, 472 239, 241, 480 241, 251, 492 251, 257, 508 257, 263, 520 263, 269, 532 269, 271, 540 271, 277, 548 277, 281, 558 281, 283, 564 283, 293, 576 293, 307, 600 307, 311, 618 311, 313, 624 313, 317, 630 317, 331, 648 331, 337, 668 337, 347, 684 347, 349, 696 349, 353, 702 353, 359, 712 359, 367, 726 367, 373, 740 373, 379, 752 379, 383, 762 383, 389, 772 389, 397, 786 397, 401, 798 401, 409, 810 409, 419, 828 419, 421, 840 421, 431, 852 431, 433, 864 433, 439, 872 439, 443, 882 443, 449, 892 449, 457, 906 457, 461, 918 461, 463, 924 463, 467, 930 467, 479, 946 479, 487, 966 487, 491, 978 491, 499, 990 499, 503, 1002 503, 509, 1012 509, 521, 1030 521, 523, 1044 523, 541, 1064 541, 547, 1088 547, 557, 1104 557, 563, 1120 563, 569, 1132 569, 571, 1140 571, 577, 1148 577, 587, 1164 587, 593, 1180 593, 599, 1192 599, 601, 1200 601, 607, 1208 607, 613, 1220 613, 617, 1230 617, 619, 1236 619, 631, 1250 631, 641, 1272 641, 643, 1284 643, 647, 1290 647, 653, 1300 653, 659, 1312 659, 661, 1320 661, 673, 1334 673, 677, 1350 677, 683, 1360 683, 691, 1374 691, 701, 1392 701, 709, 1410 709, 719, 1428 719, 727, 1446 727, 733, 1460 733, 739, 1472 739, 743, 1482 743, 751, 1494 751, 757, 1508 757, 761, 1518 761, 769, 1530 769, 773, 1542 773, 787, 1560 787, 797, 1584 797, 809, 1606 809, 811, 1620 811, 821, 1632 821, 823, 1644 823, 827, 1650 827, 829, 1656 829, 839, 1668 839, 853, 1692 853, 857, 1710 857, 859, 1716 859, 863, 1722 863, 877, 1740 877, 881, 1758 881, 883, 1764 883, 887, 1770 887, 907, 1794 907, 911, 1818 911, 919, 1830 919, 929, 1848 929, 937, 1866 937, 941, 1878 941, 947, 1888 947, 953, 1900 953, 967, 1920 967, 971, 1938 971, 977, 1948 977, 983, 1960 983, 991, 1974 991, 997, 1988 |
0, 0, 2, 2 0, 2, 3, 5 2, 3, 5, 10 3, 5, 7, 15 5, 7, 11, 23 7, 11, 13, 31 11, 13, 17, 41 13, 17, 19, 49 17, 19, 23, 59 19, 23, 29, 71 23, 29, 31, 83 29, 31, 37, 97 31, 37, 41, 109 37, 41, 43, 121 41, 43, 47, 131 43, 47, 53, 143 47, 53, 59, 159 53, 59, 61, 173 59, 61, 67, 187 61, 67, 71, 199 67, 71, 73, 211 71, 73, 79, 223 73, 79, 83, 235 79, 83, 89, 251 83, 89, 97, 269 89, 97, 101, 287 97, 101, 103, 301 101, 103, 107, 311 103, 107, 109, 319 107, 109, 113, 329 109, 113, 127, 349 113, 127, 131, 371 127, 131, 137, 395 131, 137, 139, 407 137, 139, 149, 425 139, 149, 151, 439 149, 151, 157, 457 151, 157, 163, 471 157, 163, 167, 487 163, 167, 173,
503 167, 173, 179,
519 173, 179, 181,
533 179, 181, 191,
551 181, 191, 193,
565 191, 193, 197,
581 193, 197, 199,
589 197, 199, 211,
607 199, 211, 223,
633 211, 223, 227,
661 223, 227, 229,
679 227, 229, 233,
689 229, 233, 239,
701 233, 239, 241,
713 239, 241, 251,
731 241, 251, 257,
749 251, 257, 263,
771 257, 263, 269,
789 263, 269, 271,
803 269, 271, 277,
817 271, 277, 281,
829 277, 281, 283,
841 281, 283, 293,
857 283, 293, 307,
883 293, 307, 311,
911 307, 311, 313,
931 311, 313, 317,
941 313, 317, 331,
961 317, 331, 337,
985 331, 337, 347,
1015 337, 347, 349,
1033 347, 349, 353,
1049 349, 353, 359,
1061 353, 359, 367,
1079 359, 367, 373,
1099 367, 373, 379,
1119 373, 379, 383,
1135 379, 383, 389,
1151 383, 389, 397,
1169 389, 397, 401,
1187 397, 401, 409,
1207 401, 409, 419,
1229 409, 419, 421,
1249 419, 421, 431,
1271 421, 431, 433,
1285 431, 433, 439,
1303 433, 439, 443,
1315 439, 443, 449,
1331 443, 449, 457,
1349 449, 457, 461,
1367 457, 461, 463,
1381 461, 463, 467,
1391 463, 467, 479,
1409 467, 479, 487,
1433 479, 487, 491,
1457 487, 491, 499,
1477 491, 499, 503,
1493 499, 503, 509,
1511 503, 509, 521,
1533 509, 521, 523,
1553 521, 523, 541,
1585 523, 541, 547,
1611 541, 547, 557,
1645 547, 557, 563,
1667 557, 563, 569,
1689 563, 569, 571,
1703 569, 571, 577,
1717 571, 577, 587,
1735 577, 587, 593,
1757 587, 593, 599,
1779 593, 599, 601,
1793 599, 601, 607,
1807 601, 607, 613,
1821 607, 613, 617,
1837 613, 617, 619,
1849 617, 619, 631,
1867 619, 631, 641,
1891 631, 641, 643,
1915 641, 643, 647,
1931 643, 647, 653,
1943 647, 653, 659,
1959 653, 659, 661,
1973 659, 661, 673,
1993 661, 673, 677,
2011 673, 677, 683,
2033 677, 683, 691,
2051 683, 691, 701,
2075 691, 701, 709,
2101 701, 709, 719,
2129 709, 719, 727,
2155 719, 727, 733,
2179 727, 733, 739,
2199 733, 739, 743,
2215 739, 743, 751,
2233 743, 751, 757,
2251 751, 757, 761,
2269 757, 761, 769,
2287 761, 769, 773,
2303 769, 773, 787,
2329 773, 787, 797,
2357 787, 797, 809,
2393 797, 809, 811,
2417 809, 811, 821,
2441 811, 821, 823,
2455 821, 823, 827,
2471 823, 827, 829,
2479 827, 829, 839,
2495 829, 839, 853,
2521 839, 853, 857,
2549 853, 857, 859,
2569 857, 859, 863,
2579 859, 863, 877,
2599 863, 877, 881,
2621 877, 881, 883,
2641 881, 883, 887,
2651 883, 887, 907,
2677 887, 907, 911,
2705 907, 911, 919,
2737 911, 919, 929,
2759 919, 929, 937,
2785 929, 937, 941,
2807 937, 941, 947,
2825 941, 947, 953,
2841 947, 953, 967,
2867 953, 967, 971,
2891 967, 971, 977,
2915 971, 977, 983,
2931 977, 983, 991,
2951 983, 991, 997,
2971 |
0, 0, 0, 2, 2 0, 0, 2, 3, 5 0, 2, 3, 5, 10 2, 3, 5, 7, 17 3, 5, 7, 11, 26 5, 7, 11, 13, 36 7, 11, 13, 17, 48 11, 13, 17, 19,
60 13, 17, 19, 23,
72 17, 19, 23, 29,
88 19, 23, 29, 31,
102 23, 29, 31, 37,
120 29, 31, 37, 41,
138 31, 37, 41, 43,
152 37, 41, 43, 47,
168 41, 43, 47, 53,
184 43, 47, 53, 59,
202 47, 53, 59, 61,
220 53, 59, 61, 67,
240 59, 61, 67, 71,
258 61, 67, 71, 73,
272 67, 71, 73, 79,
290 71, 73, 79, 83,
306 73, 79, 83, 89,
324 79, 83, 89, 97,
348 83, 89, 97,
101, 370 89, 97, 101,
103, 390 97, 101, 103,
107, 408 101, 103, 107,
109, 420 103, 107, 109,
113, 432 107, 109, 113,
127, 456 109, 113, 127,
131, 480 113, 127, 131,
137, 508 127, 131, 137,
139, 534 131, 137, 139,
149, 556 137, 139, 149,
151, 576 139, 149, 151,
157, 596 149, 151, 157,
163, 620 151, 157, 163,
167, 638 157, 163, 167,
173, 660 163, 167, 173,
179, 682 167, 173, 179,
181, 700 173, 179, 181,
191, 724 179, 181, 191,
193, 744 181, 191, 193,
197, 762 191, 193, 197, 199,
780 193, 197, 199,
211, 800 197, 199, 211,
223, 830 199, 211, 223,
227, 860 211, 223, 227,
229, 890 223, 227, 229,
233, 912 227, 229, 233,
239, 928 229, 233, 239,
241, 942 233, 239, 241,
251, 964 239, 241, 251,
257, 988 241, 251, 257,
263, 1012 251, 257, 263,
269, 1040 257, 263, 269,
271, 1060 263, 269, 271,
277, 1080 269, 271, 277,
281, 1098 271, 277, 281,
283, 1112 277, 281, 283,
293, 1134 281, 283, 293,
307, 1164 283, 293, 307,
311, 1194 293, 307, 311,
313, 1224 307, 311, 313,
317, 1248 311, 313, 317,
331, 1272 313, 317, 331,
337, 1298 317, 331, 337,
347, 1332 331, 337, 347,
349, 1364 337, 347, 349,
353, 1386 347, 349, 353,
359, 1408 349, 353, 359,
367, 1428 353, 359, 367,
373, 1452 359, 367, 373,
379, 1478 367, 373, 379,
383, 1502 373, 379, 383, 389,
1524 379, 383, 389,
397, 1548 383, 389, 397,
401, 1570 389, 397, 401,
409, 1596 397, 401, 409,
419, 1626 401, 409, 419,
421, 1650 409, 419, 421,
431, 1680 419, 421, 431,
433, 1704 421, 431, 433,
439, 1724 431, 433, 439,
443, 1746 433, 439, 443,
449, 1764 439, 443, 449,
457, 1788 443, 449, 457,
461, 1810 449, 457, 461,
463, 1830 457, 461, 463,
467, 1848 461, 463, 467,
479, 1870 463, 467, 479,
487, 1896 467, 479, 487,
491, 1924 479, 487, 491,
499, 1956 487, 491, 499,
503, 1980 491, 499, 503,
509, 2002 499, 503, 509,
521, 2032 503, 509, 521,
523, 2056 509, 521, 523,
541, 2094 521, 523, 541,
547, 2132 523, 541, 547,
557, 2168 541, 547, 557,
563, 2208 547, 557, 563,
569, 2236 557, 563, 569,
571, 2260 563, 569, 571,
577, 2280 569, 571, 577,
587, 2304 571, 577, 587,
593, 2328 577, 587, 593,
599, 2356 587, 593, 599,
601, 2380 593, 599, 601,
607, 2400 599, 601, 607,
613, 2420 601, 607, 613,
617, 2438 607, 613, 617,
619, 2456 613, 617, 619,
631, 2480 617, 619, 631,
641, 2508 619, 631, 641,
643, 2534 631, 641, 643,
647, 2562 641, 643, 647,
653, 2584 643, 647, 653,
659, 2602 647, 653, 659,
661, 2620 653, 659, 661,
673, 2646 659, 661, 673,
677, 2670 661, 673, 677,
683, 2694 673, 677, 683,
691, 2724 677, 683, 691,
701, 2752 683, 691, 701,
709, 2784 691, 701, 709, 719,
2820 701, 709, 719,
727, 2856 709, 719, 727,
733, 2888 719, 727, 733,
739, 2918 727, 733, 739,
743, 2942 733, 739, 743,
751, 2966 739, 743, 751,
757, 2990 743, 751, 757,
761, 3012 751, 757, 761,
769, 3038 757, 761, 769,
773, 3060 761, 769, 773,
787, 3090 769, 773, 787,
797, 3126 773, 787, 797,
809, 3166 787, 797, 809,
811, 3204 797, 809, 811,
821, 3238 809, 811, 821,
823, 3264 811, 821, 823,
827, 3282 821, 823, 827,
829, 3300 823, 827, 829,
839, 3318 827, 829, 839,
853, 3348 829, 839, 853,
857, 3378 839, 853, 857,
859, 3408 853, 857, 859,
863, 3432 857, 859, 863,
877, 3456 859, 863, 877,
881, 3480 863, 877, 881,
883, 3504 877, 881, 883,
887, 3528 881, 883, 887,
907, 3558 883, 887, 907,
911, 3588 887, 907, 911,
919, 3624 907, 911, 919,
929, 3666 911, 919, 929,
937, 3696 919, 929, 937,
941, 3726 929, 937, 941,
947, 3754 937, 941, 947,
953, 3778 941, 947, 953,
967, 3808 947, 953, 967,
971, 3838 953, 967, 971,
977, 3868 967, 971, 977,
983, 3898 971, 977, 983,
991, 3922 977, 983, 991,
997, 3948 |
0, 0, 0, 0, 2, 2 0, 0, 0, 2, 3, 5 0, 0, 2, 3, 5, 10 0, 2, 3, 5, 7, 17 2, 3, 5, 7, 11,
28 3, 5, 7, 11,
13, 39 5, 7, 11, 13,
17, 53 7, 11, 13, 17,
19, 67 11, 13, 17, 19,
23, 83 13, 17, 19, 23,
29, 101 17, 19, 23, 29,
31, 119 19, 23, 29, 31,
37, 139 23, 29, 31, 37,
41, 161 29, 31, 37, 41,
43, 181 31, 37, 41, 43,
47, 199 37, 41, 43, 47,
53, 221 41, 43, 47, 53,
59, 243 43, 47, 53, 59,
61, 263 47, 53, 59, 61,
67, 287 53, 59, 61, 67,
71, 311 59, 61, 67, 71,
73, 331 61, 67, 71, 73,
79, 351 67, 71, 73, 79,
83, 373 71, 73, 79, 83,
89, 395 73, 79, 83, 89,
97, 421 79, 83, 89, 97,
101, 449 83, 89, 97,
101, 103, 473 89, 97, 101,
103, 107, 497 97, 101, 103,
107, 109, 517 101, 103, 107,
109, 113, 533 103, 107, 109,
113, 127, 559 107, 109, 113,
127, 131, 587 109, 113, 127,
131, 137, 617 113, 127, 131,
137, 139, 647 127, 131, 137,
139, 149, 683 131, 137, 139,
149, 151, 707 137, 139, 149,
151, 157, 733 139, 149, 151,
157, 163, 759 149, 151, 157,
163, 167, 787 151, 157, 163,
167, 173, 811 157, 163, 167,
173, 179, 839 163, 167, 173,
179, 181, 863 167, 173, 179,
181, 191, 891 173, 179, 181,
191, 193, 917 179, 181, 191,
193, 197, 941 181, 191, 193,
197, 199, 961 191, 193, 197,
199, 211, 991 193, 197, 199,
211, 223, 1023 197, 199, 211,
223, 227, 1057 199, 211, 223,
227, 229, 1089 211, 223, 227,
229, 233, 1123 223, 227, 229,
233, 239, 1151 227, 229, 233,
239, 241, 1169 229, 233, 239,
241, 251, 1193 233, 239, 241,
251, 257, 1221 239, 241, 251,
257, 263, 1251 241, 251, 257,
263, 269, 1281 251, 257, 263,
269, 271, 1311 257, 263, 269,
271, 277, 1337 263, 269, 271,
277, 281, 1361 269, 271, 277,
281, 283, 1381 271, 277, 281,
283, 293, 1405 277, 281, 283,
293, 307, 1441 281, 283, 293,
307, 311, 1475 283, 293, 307,
311, 313, 1507 293, 307, 311,
313, 317, 1541 307, 311, 313, 317,
331, 1579 311, 313, 317,
331, 337, 1609 313, 317, 331,
337, 347, 1645 317, 331, 337,
347, 349, 1681 331, 337, 347,
349, 353, 1717 337, 347, 349,
353, 359, 1745 347, 349, 353,
359, 367, 1775 349, 353, 359,
367, 373, 1801 353, 359, 367,
373, 379, 1831 359, 367, 373,
379, 383, 1861 367, 373, 379,
383, 389, 1891 373, 379, 383,
389, 397, 1921 379, 383, 389,
397, 401, 1949 383, 389, 397,
401, 409, 1979 389, 397, 401,
409, 419, 2015 397, 401, 409,
419, 421, 2047 401, 409, 419,
421, 431, 2081 409, 419, 421,
431, 433, 2113 419, 421, 431,
433, 439, 2143 421, 431, 433,
439, 443, 2167 431, 433, 439,
443, 449, 2195 433, 439, 443,
449, 457, 2221 439, 443, 449,
457, 461, 2249 443, 449, 457,
461, 463, 2273 449, 457, 461,
463, 467, 2297 457, 461, 463,
467, 479, 2327 461, 463, 467,
479, 487, 2357 463, 467, 479,
487, 491, 2387 467, 479, 487,
491, 499, 2423 479, 487, 491,
499, 503, 2459 487, 491, 499,
503, 509, 2489 491, 499, 503,
509, 521, 2523 499, 503, 509,
521, 523, 2555 503, 509, 521,
523, 541, 2597 509, 521, 523,
541, 547, 2641 521, 523, 541,
547, 557, 2689 523, 541, 547,
557, 563, 2731 541, 547, 557,
563, 569, 2777 547, 557, 563,
569, 571, 2807 557, 563, 569,
571, 577, 2837 563, 569, 571,
577, 587, 2867 569, 571, 577,
587, 593, 2897 571, 577, 587,
593, 599, 2927 577, 587, 593,
599, 601, 2957 587, 593, 599,
601, 607, 2987 593, 599, 601,
607, 613, 3013 599, 601, 607,
613, 617, 3037 601, 607, 613,
617, 619, 3057 607, 613, 617,
619, 631, 3087 613, 617, 619,
631, 641, 3121 617, 619, 631,
641, 643, 3151 619, 631, 641, 643,
647, 3181 631, 641, 643,
647, 653, 3215 641, 643, 647,
653, 659, 3243 643, 647, 653,
659, 661, 3263 647, 653, 659,
661, 673, 3293 653, 659, 661,
673, 677, 3323 659, 661, 673,
677, 683, 3353 661, 673, 677,
683, 691, 3385 673, 677, 683,
691, 701, 3425 677, 683, 691,
701, 709, 3461 683, 691, 701,
709, 719, 3503 691, 701, 709,
719, 727, 3547 701, 709, 719,
727, 733, 3589 709, 719, 727,
733, 739, 3627 719, 727, 733,
739, 743, 3661 727, 733, 739,
743, 751, 3693 733, 739, 743,
751, 757, 3723 739, 743, 751,
757, 761, 3751 743, 751, 757,
761, 769, 3781 751, 757, 761,
769, 773, 3811 757, 761, 769,
773, 787, 3847 761, 769, 773,
787, 797, 3887 769, 773, 787,
797, 809, 3935 773, 787, 797,
809, 811, 3977 787, 797, 809,
811, 821, 4025 797, 809, 811,
821, 823, 4061 809, 811, 821,
823, 827, 4091 811, 821, 823,
827, 829, 4111 821, 823, 827,
829, 839, 4139 823, 827, 829,
839, 853, 4171 827, 829, 839,
853, 857, 4205 829, 839, 853,
857, 859, 4237 839, 853, 857,
859, 863, 4271 853, 857, 859,
863, 877, 4309 857, 859, 863, 877,
881, 4337 859, 863, 877,
881, 883, 4363 863, 877, 881,
883, 887, 4391 877, 881, 883,
887, 907, 4435 881, 883, 887,
907, 911, 4469 883, 887, 907,
911, 919, 4507 887, 907, 911,
919, 929, 4553 907, 911, 919,
929, 937, 4603 911, 919, 929,
937, 941, 4637 919, 929, 937,
941, 947, 4673 929, 937, 941,
947, 953, 4707 937, 941, 947,
953, 967, 4745 941, 947, 953,
967, 971, 4779 947, 953, 967,
971, 977, 4815 953, 967, 971,
977, 983, 4851 967, 971, 977,
983, 991, 4889 971, 977, 983,
991, 997, 4919 |
T
|
Six |
Sept |
Huit |
|
2, 3, 5, 7, 11,
13, 41 3, 5, 7, 11,
13, 17, 56 5, 7, 11, 13,
17, 19, 72 7, 11, 13, 17,
19, 23, 90 11, 13, 17, 19,
23, 29, 112 13, 17, 19, 23,
29, 31, 132 17, 19, 23, 29,
31, 37, 156 19, 23, 29, 31,
37, 41, 180 23, 29, 31, 37,
41, 43, 204 29, 31, 37, 41,
43, 47, 228 31, 37, 41, 43,
47, 53, 252 37, 41, 43, 47,
53, 59, 280 41, 43, 47, 53,
59, 61, 304 43, 47, 53, 59,
61, 67, 330 47, 53, 59, 61,
67, 71, 358 53, 59, 61, 67,
71, 73, 384 59, 61, 67, 71,
73, 79, 410 61, 67, 71, 73,
79, 83, 434 67, 71, 73, 79,
83, 89, 462 71, 73, 79, 83,
89, 97, 492 |
2, 3, 5, 7, 11,
13, 17, 58 3, 5, 7, 11,
13, 17, 19, 75 5, 7, 11, 13,
17, 19, 23, 95 7, 11, 13, 17,
19, 23, 29, 119 11, 13, 17, 19,
23, 29, 31, 143 13, 17, 19, 23,
29, 31, 37, 169 17, 19, 23, 29,
31, 37, 41, 197 19, 23, 29, 31,
37, 41, 43, 223 23, 29, 31, 37,
41, 43, 47, 251 29, 31, 37, 41,
43, 47, 53, 281 31, 37, 41, 43,
47, 53, 59, 311 37, 41, 43, 47,
53, 59, 61, 341 41, 43, 47, 53,
59, 61, 67, 371 43, 47, 53, 59,
61, 67, 71, 401 47, 53, 59, 61,
67, 71, 73, 431 53, 59, 61, 67,
71, 73, 79, 463 59, 61, 67, 71,
73, 79, 83, 493 61, 67, 71, 73,
79, 83, 89, 523 67, 71, 73, 79,
83, 89, 97, 559 |
2, 3, 5, 7, 11,
13, 17, 19, 77 3, 5, 7, 11,
13, 17, 19, 23, 98 5, 7, 11, 13,
17, 19, 23, 29, 124 7, 11, 13, 17,
19, 23, 29, 31, 150 11, 13, 17, 19,
23, 29, 31, 37, 180 13, 17, 19, 23,
29, 31, 37, 41, 210 17, 19, 23, 29,
31, 37, 41, 43, 240 19, 23, 29, 31,
37, 41, 43, 47, 270 23, 29, 31, 37,
41, 43, 47, 53, 304 29, 31, 37, 41,
43, 47, 53, 59, 340 31, 37, 41, 43,
47, 53, 59, 61, 372 37, 41, 43, 47,
53, 59, 61, 67, 408 41, 43, 47, 53,
59, 61, 67, 71, 442 43, 47, 53, 59,
61, 67, 71, 73, 474 47, 53, 59, 61,
67, 71, 73, 79, 510 53, 59, 61, 67,
71, 73, 79, 83, 546 59, 61, 67, 71,
73, 79, 83, 89, 582 61, 67, 71, 73,
79, 83, 89, 97, 620 |
|
Neuf |
Dix |
|
2, 3, 5, 7, 11,
13, 17, 19, 23, 100 3, 5, 7, 11,
13, 17, 19, 23, 29, 127 5, 7, 11, 13,
17, 19, 23, 29, 31, 155 7, 11, 13, 17,
19, 23, 29, 31, 37, 187 11, 13, 17, 19,
23, 29, 31, 37, 41, 221 13, 17, 19, 23,
29, 31, 37, 41, 43, 253 17, 19, 23, 29,
31, 37, 41, 43, 47, 287 19, 23, 29, 31,
37, 41, 43, 47, 53, 323 23, 29, 31, 37,
41, 43, 47, 53, 59, 363 29, 31, 37, 41,
43, 47, 53, 59, 61, 401 31, 37, 41, 43,
47, 53, 59, 61, 67, 439 37, 41, 43, 47,
53, 59, 61, 67, 71, 479 41, 43, 47, 53,
59, 61, 67, 71, 73, 515 43, 47, 53, 59,
61, 67, 71, 73, 79, 553 47, 53, 59, 61,
67, 71, 73, 79, 83, 593 53, 59, 61, 67,
71, 73, 79, 83, 89, 635 59, 61, 67, 71,
73, 79, 83, 89, 97, 679 |
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 129 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 158 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 192 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 228 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 264 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 300 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 340 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 382 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 424 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 468 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 510 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 552 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 594 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 636 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 682 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 732 |
|
Onze |
Douze |
|
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 160 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 195 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 233 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 271 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 311 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 353 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 399 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 443 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 491 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 539 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 583 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 631 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 677 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 725 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97, 779 |
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 197 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 236 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 276 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 47, 318 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53, 364 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59, 412 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 460 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 510 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 562 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 612 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 662 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 714 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 766 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 822 |
|
Treize |
Qu |
|
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 238 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 279 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 323 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 47, 53, 371 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53, 59, 423 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59, 61, 473 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 527 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 581 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 73, 635 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 691 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 745 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 803 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97, 863 |
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 281 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 326 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 376 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 430 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 484 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 540 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 598 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 654 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 714 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 774 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 834 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 900 |
|
Quinze |
Seize |
|
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 328 3, 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 379 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 435 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 491 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 551 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 611 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 671 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 733 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 797 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 863 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 931 |
2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 381 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 438 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 496 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 558 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 622 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 684 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 750 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 816 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 886 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 960 |
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Exemples en rouge
pour les sommes de 16 premiers telles qu'indiquées dans la table juste
au-dessus. Somme S de k
premier, le dernier étant n. |
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TOUS k, n, S 1, 2, 2 2, 3, 5 3, 5, 10 4, 7, 17 5, 11, 28 6, 13, 41 7, 17, 58 8, 19, 77 9, 23, 100 10, 29, 129 11, 31, 160 12, 37, 197 13, 41, 238 14, 43, 281 15, 47, 328 16, 53, 381 17, 59, 440 18, 61, 501 19, 67, 568 20, 71, 639 21, 73, 712 22, 79, 791 23, 83, 874 24, 89, 963 25, 97, 1060 26, 101, 1161 27, 103, 1264 28, 107, 1371 29, 109, 1480 30, 113, 1593 31, 127, 1720 32, 131, 1851 33, 137, 1988 34, 139, 2127 35, 149, 2276 36, 151, 2427 37, 157, 2584 38, 163, 2747 39, 167, 2914 40, 173, 3087 41, 179, 3266 42, 181, 3447 43, 191, 3638 44, 193, 3831 45, 197, 4028 46, 199, 4227 47, 211, 4438 48, 223, 4661 49, 227, 4888 50, 229, 5117 51, 233, 5350 52, 239, 5589 53, 241, 5830 54, 251, 6081 55, 257, 6338 56, 263, 6601 57, 269, 6870 58, 271, 7141 59, 277, 7418 60, 281, 7699 61, 283, 7982 62, 293, 8275 63, 307, 8582 64, 311, 8893 65, 313, 9206 66, 317, 9523 67, 331, 9854 68, 337, 10191 69, 347, 10538 70, 349, 10887 71, 353, 11240 72, 359, 11599 73, 367, 11966 74, 373, 12339 75, 379, 12718 76, 383, 13101 77, 389, 13490 78, 397, 13887 79, 401, 14288 80, 409, 14697 81, 419, 15116 82, 421, 15537 83, 431, 15968 84, 433, 16401 85, 439, 16840 86, 443, 17283 87, 449, 17732 88, 457, 18189 89, 461, 18650 90, 463, 19113 91, 467, 19580 92, 479, 20059 93, 487, 20546 94, 491, 21037 95, 499, 21536 96, 503, 22039 97, 509, 22548 98, 521, 23069 99, 523, 23592 100, 541, 24133 101, 547, 24680 102, 557, 25237 103, 563, 25800 104, 569, 26369 105, 571, 26940 106, 577, 27517 107, 587, 28104 108, 593, 28697 109, 599, 29296 110, 601, 29897 111, 607, 30504 112, 613, 31117 113, 617, 31734 114, 619, 32353 115, 631, 32984 116, 641, 33625 117, 643, 34268 118, 647, 34915 119, 653, 35568 120, 659, 36227 121, 661, 36888 122, 673, 37561 123, 677, 38238 124, 683, 38921 125, 691, 39612 126, 701, 40313 127, 709, 41022 128, 719, 41741 129, 727, 42468 130, 733, 43201 131, 739, 43940 132, 743, 44683 133, 751, 45434 134, 757, 46191 135, 761, 46952 136, 769, 47721 137, 773, 48494 138, 787, 49281 139, 797, 50078 140, 809, 50887 141, 811, 51698 142, 821, 52519 143, 823, 53342 144, 827, 54169 145, 829, 54998 146, 839, 55837 147, 853, 56690 148, 857, 57547 149, 859, 58406 150, 863, 59269 151, 877, 60146 152, 881, 61027 153, 883, 61910 154, 887, 62797 155, 907, 63704 156, 911, 64615 157, 919, 65534 158, 929, 66463 159, 937, 67400 160, 941, 68341 161, 947, 69288 162, 953, 70241 163, 967, 71208 164, 971, 72179 165, 977, 73156 166, 983, 74139 167, 991, 75130 168, 997, 76127 169, 1009, 77136 |
IMPAIRS k, n, S 1, 3, 3 2, 5, 8 3, 7, 15 4, 11, 26 5, 13, 39 6, 17, 56 7, 19, 75 8, 23, 98 9, 29, 127 10, 31, 158 11, 37, 195 12, 41, 236 13, 43, 279 14, 47, 326 15, 53, 379 16, 59, 438 17, 61, 499 18, 67, 566 19, 71, 637 20, 73, 710 21, 79, 789 22, 83, 872 23, 89, 961 24, 97, 1058 25, 101, 1159 26, 103, 1262 27, 107, 1369 28, 109, 1478 29, 113, 1591 30, 127, 1718 31, 131, 1849 32, 137, 1986 33, 139, 2125 34, 149, 2274 35, 151, 2425 36, 157, 2582 37, 163, 2745 38, 167, 2912 39, 173, 3085 40, 179, 3264 41, 181, 3445 42, 191, 3636 43, 193, 3829 44, 197, 4026 45, 199, 4225 46, 211, 4436 47, 223, 4659 48, 227, 4886 49, 229, 5115 50, 233, 5348 51, 239, 5587 52, 241, 5828 53, 251, 6079 54, 257, 6336 55, 263, 6599 56, 269, 6868 57, 271, 7139 58, 277, 7416 59, 281, 7697 60, 283, 7980 61, 293, 8273 62, 307, 8580 63, 311, 8891 64, 313, 9204 65, 317, 9521 66, 331, 9852 67, 337, 10189 68, 347, 10536 69, 349, 10885 70, 353, 11238 71, 359, 11597 72, 367, 11964 73, 373, 12337 74, 379, 12716 75, 383, 13099 76, 389, 13488 77, 397, 13885 78, 401, 14286 79, 409, 14695 80, 419, 15114 81, 421, 15535 82, 431, 15966 83, 433, 16399 84, 439, 16838 85, 443, 17281 86, 449, 17730 87, 457, 18187 88, 461, 18648 89, 463, 19111 90, 467, 19578 91, 479, 20057 92, 487, 20544 93, 491, 21035 94, 499, 21534 95, 503, 22037 96, 509, 22546 97, 521, 23067 98, 523, 23590 99, 541, 24131 100, 547, 24678 101, 557, 25235 102, 563, 25798 103, 569, 26367 104, 571, 26938 105, 577, 27515 106, 587, 28102 107, 593, 28695 108, 599, 29294 109, 601, 29895 110, 607, 30502 111, 613, 31115 112, 617, 31732 113, 619, 32351 114, 631, 32982 115, 641, 33623 116, 643, 34266 117, 647, 34913 118, 653, 35566 119, 659, 36225 120, 661, 36886 121, 673, 37559 122, 677, 38236 123, 683, 38919 124, 691, 39610 125, 701, 40311 126, 709, 41020 127, 719, 41739 128, 727, 42466 129, 733, 43199 130, 739, 43938 131, 743, 44681 132, 751, 45432 133, 757, 46189 134, 761, 46950 135, 769, 47719 136, 773, 48492 137, 787, 49279 138, 797, 50076 139, 809, 50885 140, 811, 51696 141, 821, 52517 142, 823, 53340 143, 827, 54167 144, 829, 54996 145, 839, 55835 146, 853, 56688 147, 857, 57545 148, 859, 58404 149, 863, 59267 150, 877, 60144 151, 881, 61025 152, 883, 61908 153, 887, 62795 154, 907, 63702 155, 911, 64613 156, 919, 65532 157, 929, 66461 158, 937, 67398 159, 941, 68339 160, 947, 69286 161, 953, 70239 162, 967, 71206 163, 971, 72177 164, 977, 73154 165, 983, 74137 166, 991, 75128 167, 997, 76125 168, 1009, 77134 |
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Somme de 2 à 5 premiers consécutifs à la puissance 1 à 5
Exemple: 5 = 21 + 31,
13 = 22 + 32, 35 = 23 + 33… 10 = 21
+ 31 + 51, 38 = 22 + 32 + 52
…
Somme des Q premiers consécutifs de 1 à P à la puissance 1 à 5
Exemple: Somme des cubes des quatre premiers nombres premiers = 503
23 + 33 + 53 + 73 = 503
Tableau pour les 25 premiers jusqu'à n = 100
Voir Sommes et produits des nombres
premiers
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Voir |
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